A Semidefinite Relaxation Approach for Fair Graph Clustering

TL;DR

This paper presents a novel semidefinite relaxation method for fair graph clustering that balances clustering accuracy with fairness constraints, addressing biases in network analysis.

Contribution

It introduces a new optimization framework for fair clustering, employing semidefinite relaxation and scalable algorithms for different graph sizes.

Findings

Outperforms existing methods in accuracy-fairness trade-off

Effective for medium-sized and large graphs

Demonstrates superiority on stochastic block model graphs

Abstract

Fair graph clustering is crucial for ensuring equitable representation and treatment of diverse communities in network analysis. Traditional methods often ignore disparities among social, economic, and demographic groups, perpetuating biased outcomes and reinforcing inequalities. This study introduces fair graph clustering within the framework of the disparate impact doctrine, treating it as a joint optimization problem integrating clustering quality and fairness constraints. Given the NP-hard nature of this problem, we employ a semidefinite relaxation approach to approximate the underlying optimization problem. For up to medium-sized graphs, we utilize a singular value decomposition-based algorithm, while for larger graphs, we propose a novel algorithm based on the alternative direction method of multipliers. Unlike existing methods, our formulation allows for tuning the trade-off between clustering quality and fairness. Experimental results on graphs generated from the standard stochastic block model demonstrate the superiority of our approach in achieving an optimal accuracy-fairness trade-off compared to state-of-the-art methods.